Question

1.Two groups are having competition for chase. If one plays it in its own campus it will win with probability P> ½. They will play three times, two in group 1’s campus and one in group 2’s campus. If one wins game 1 and 2, then game 3 is not going to be played. a) What is P[T], the probability that the group 1 wins the series? b) If they play only once will group 1 have higher chance of winning than from playing 3 games? [5 + 5 = 10]

Answer 1

a) Group 1 wins the series iff it wins the first two times in it's own campus or it loses in exactly one of the first two games and wins the third.

Now,  , and

Thus P(Group 1 wins the series) = (ANS.)

(b)

If the only 1 game was played on Group 1's own campus, then their probability of winning would have been

This is better than playing the 3 games if and only if:

Hence by playing only 1 game in it's own campus, Group 1 has higher probability of winning than that by playing the 3 games.